ORBITS OF THE NEARBY GALAXIES

A numerical application of the action variational principle is used to study solutions for the relative motions of the nearby galaxies and groups of galaxies treated as tracers of the mass within distance R less than or similar to 4 Mpc. This paper is meant to be a more detailed account than has been given previously of the computations and the nature of the solutions for a somewhat larger sample of the nearby galaxies. Rather than following the gradient of the action to a minimum with respect to variation of the orbit parameters, as has been done in most previous applications of this method, the solutions are found by matrix inversion. Matrix inversion can more fairly sample the range of solutions, and it applies equally well to the prediction of distances given redshifts or of redshifts given distances. The latter, which is the main subject of this paper, have relatively small scatter among the set of solutions, and the predicted redshifts agree quite well with observations when the galaxies are assigned a mass-to-light ratio of approximately 150 M./L. This result, which includes the mass between groups, is not very sensitive to the choices of Hubble's constant and the cosmological density parameter within the ranges currently under discussion. In the solutions the interaction with neighboring groups can make the present transverse velocity of the Milky Way relative to M31 comparable to the radial velocity of approach, the projected minimum separation of the Milky Way and M31 typically being in the range 250-400 kpc. The predicted peculiar velocity of the Milky Way relative to the mean for the matter at R less than or similar to 4 Mpc has significant scatter among the set of solutions and can be consistent with the observations.